87 research outputs found

    Asymptotic Estimates for Second Kind Generalized Stirling Numbers

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    Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established. The generalizations of Stirling numbers considered here are generalizations along the line of Hsu and Shuie's unified generalization

    ASYMPTOTIC ESTIMATES FOR GENERALIZED STIRLING NUMBERS

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    Asymptotic Estimates for r

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    The r-Whitney numbers of the second kind are a generalization of all the Stirling-type numbers of the second kind which are in line with the unified generalization of Hsu and Shuie. In this paper, asymptotic formulas for r-Whitney numbers of the second kind with integer and real parameters are obtained and the range of validity of each formula is established

    Matrix models for stationary Gromov-Witten invariants of the Riemann sphere

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    Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of P1\mathbb{P}^1 as an isomonodromic tau function associated with a difference equation. As a byproduct we obtain an analogue of the Kontsevich matrix model for this tau function. A connection with the Charlier ensemble is also considered.Comment: v3: new appendix
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